block of glass or any transparent medium is

called a Prism; and these 4

would be section-views of different kinds of prisms, the size of the angle or length of its sides being immaterial. Now what will happen to a ray passing through a prism, supposed denser than the surrounding medium? All will depend as usual on the directions of P and p, and

these will not be parallel, as the surfaces are inclined to one another. Ray A refracted towards P proceeds to p; refracted

there from p goes on to C.

The angle between AP and pC, the first and last directions

of the ray, is the angle of devia

tion.

It will be evident that this increases with the increase of either the angle of the sides or the density of the prism, or both. All this would of course be reversed in a prism formed of a rarer surrounded by a denser medium. You will readily see that any object viewed through a prism will appear considerably out of its place: and that in whatever direction the prism may be placed, edge up, down, or sideways, the final deviation will be the same, towards the thickest

part, but following the position of the prism, and exactly corresponding with it. This must be carefully attended to, as it will immediately lead us on to something else, as we proceed from plane to convex and concave refracting surfaces.

Supposing that we were to place three prisms (or pieces of prisms—the same in practice) of dense material, as glass, one above another. It is plain that the angles might be so proportioned as to bring the refracted or emergent

rays all to one point; and if such an arrangement were turned upside down, or in any sideway position, the effect would be the same, as of course would be shown by turning the page round. But we may as soon fancy 30 prisms as 3, or 30,000 if we please; and then we should get so close an approach to a curved surface that we could not distinguish them in practice; and a surface of glass, or crystal, or diamond, equally curved upwards, downwards, sideways, and in every possible direction, would be found to re

fract all incident rays to one point. It has been ascertained, fortunately for the construction of optical instruments, most of which require large pencils of rays to be brought to a point, that a portion of a sphere, which is easily worked, answers very nearly, though not with mathematical correctness; and pieces of glass so shaped that their surfaces form portions of a sphere are called Lenses. But if a lens with two convex and spherical surfaces would be the result of an indefinite, or, as mathematicians speak,

an infinite number of prisms arranged edge outwards as above, then if we were to make the prisms of the opposite form, the thickest having the most inclined sides and the outermost position, an infinite number of these would form a spherical lens as before, but of the reverse form, concave instead of convex, having opposite properties, and making the rays, not to converge towards an actual point, but to diverge, as the dotted lines show, from a virtual or imaginary

one.

There are therefore two distinct kinds of lenses, the convex and the concave, the convex refracting inwards, the concave outwards; and four forms of each, shown edgeways thus:

where it will be noted, that for clearness of explanation the most curved side, or, as opticians term it, the deepest, is of the same radius in every case; though of course it need not have been so.

No. 1. Equi-convex, two slices, as it were, put together from spheres of the same size. No. 2. Unequally convex, or in opticians' language, "crossed," in which one side has a longer radius, that is, is a portion of a larger sphere, than the

E

other 1. Of this form of course there may be varieties innumerable, and we can suppose one of the sides gradually flattened, till at last when its radius becomes infinite, that is indefinitely great, it may be considered a plane. This will be No. 3, the plano-convex lens, which is the equi-convex slit in two. Now if we continue to push in, as it were, the flattened side, we shall make it more and more concave, as in No. 4, the Meniscus, so called from a Greek word signifying the Moon. Here we should find that so long as the convex surface has the shorter radius, its Ps, converging (or diverging as you choose to take it) the more rapidly of the two, will produce the greater angles and the stronger refraction, and the convex predominating over the concave action, the meniscus takes rank accordingly, with a convexity which is the difference, instead of the sum, of the two refractions. In one curious case, when the curves are so proportioned that the rays fall perpendicularly upon the second surface, all the refraction is done by the first. If we were to deepen the concave till its radius were equal to that of the convex, we should get a watchglass, a form with no optical property, except distortion towards the edges; like a piece of

1 Nos. 1 and 2 are both frequently called double convex.